The continuous fractional calculus has a long history within the broad area of mathematical
analysis. Indeed, it is nearly as old as the familiar integer-order calculus. Since its inception …

The subject of fractional calculus and its applications (that is, convolution-type pseudo-
differential operators including integrals and derivatives of any arbitrary real or complex …

This invaluable book provides a broad introduction to the fascinating and beautiful subject of
Fractional Calculus of Variations (FCV). In 1996, FVC evolved in order to better describe non …

We introduce a discrete-time fractional calculus of variations on the time scale (hZ) a, a∈ R,
h> 0. First and second order necessary optimality conditions are established. Examples …

We prove optimality conditions for different variational functionals containing left and right
Caputo fractional derivatives. A sufficient condition of minimization under an appropriate …

The recent theory of fractional h-difference equations introduced in [9], is enriched with
useful tools for the explicit solution of discrete equations involving left and right fractional …

This book fills a gap in the literature by introducing numerical techniques to solve problems
of fractional calculus of variations (FCV). In most cases, finding the analytic solution to such …

The review is devoted to using the fractional integro-differential calculus for description of
the dynamics of various systems and control processes. Consideration was given to the …

We introduce a discrete-time fractional calculus of variations. First and second order
necessary optimality conditions are established. Examples illustrating the use of the new …

A novel approximate analytical technique for determining the non-stationary response
probability density function (PDF) of randomly excited linear and nonlinear oscillators …